Research Trends in Collaborative Drones.

The last decade has seen an explosion of interest in drones-introducing new networking technologies, such as 5G wireless connectivity and cloud computing. The resulting advancements in communication capabilities are already expanding the ubiquitous role of drones as primary solution enablers, from search and rescue missions to information gathering and parcel delivery. Their numerous applications encompass all aspects of everyday life. Our focus is on networked and collaborative drones. The available research literature on this topic is vast. No single survey article could do justice to all critical issues. Our goal in this article is not to cover everything and include everybody but rather to offer a personal perspective on a few selected research topics that might lead to fruitful future investigations that could play an essential role in developing drone technologies. The topics we address include distributed computing with drones for the management of anonymity, countering threats posed by drones, target recognition, navigation under uncertainty, risk avoidance, and cellular technologies. Our approach is selective. Every topic includes an explanation of the problem, a discussion of a potential research methodology, and ideas for future research.

GPS-Free, Error Tolerant Path Planning for Swarms of Micro Aerial Vehicles with Quality Amplification ‡.

We present an error tolerant path planning algorithm for Micro Aerial Vehicle (MAV) swarms. We assume navigation without GPS-like techniques. The MAVs find their path using sensors and cameras, identifying and following a series of visual landmarks. The visual landmarks lead the MAVs towards their destination. MAVs are assumed to be unaware of the terrain and locations of the landmarks. They hold a priori information about landmarks, whose interpretation is prone to errors. Errors are of two types, recognition or advice. Recognition errors follow from misinterpretation of sensed data or a priori information, or confusion of objects, e.g., due to faulty sensors. Advice errors are consequences of outdated or wrong information about landmarks, e.g., due to weather conditions. Our path planning algorithm is cooperative. MAVs communicate and exchange information wirelessly, to minimize the number of recognition and advice errors. Hence, the quality of the navigation decision process is amplified. Our solution successfully achieves an adaptive error tolerant navigation system. Quality amplification is parameterized with respect to the number of MAVs. We validate our approach with theoretical proofs and numeric simulations.

Asymptotic number of hairpins of saturated RNA secondary structures.

In the absence of chaperone molecules, RNA folding is believed to depend on the distribution of kinetic traps in the energy landscape of all secondary structures. Kinetic traps in the Nussinov energy model are precisely those secondary structures that are saturated, meaning that no base pair can be added without introducing either a pseudoknot or base triple. In this paper, we compute the asymptotic expected number of hairpins in saturated structures. For instance, if every hairpin is required to contain at least θ=3 unpaired bases and the probability that any two positions can base-pair is p=3/8, then the asymptotic number of saturated structures is 1.34685[Symbol: see text]n (-3/2)[Symbol: see text]1.62178 (n) , and the asymptotic expected number of hairpins follows a normal distribution with mean [Formula: see text]. Similar results are given for values θ=1,3, and p=1,1/2,3/8; for instance, when θ=1 and p=1, the asymptotic expected number of hairpins in saturated secondary structures is 0.123194[Symbol: see text]n, a value greater than the asymptotic expected number 0.105573[Symbol: see text]n of hairpins over all secondary structures. Since RNA binding targets are often found in hairpin regions, it follows that saturated structures present potentially more binding targets than nonsaturated structures, on average. Next, we describe a novel algorithm to compute the hairpin profile of a given RNA sequence: given RNA sequence a 1,…,a n , for each integer k, we compute that secondary structure S k having minimum energy in the Nussinov energy model, taken over all secondary structures having k hairpins. We expect that an extension of our algorithm to the Turner energy model may provide more accurate structure prediction for particular RNAs, such as tRNAs and purine riboswitches, known to have a particular number of hairpins. Mathematica(™) computations, C and Python source code, and additional supplementary information are available at the website http://bioinformatics.bc.edu/clotelab/RNAhairpinProfile/ .

Asymptotic structural properties of quasi-random saturated structures of RNA.

BACKGROUND: RNA folding depends on the distribution of kinetic traps in the landscape of all secondary structures. Kinetic traps in the Nussinov energy model are precisely those secondary structures that are saturated, meaning that no base pair can be added without introducing either a pseudoknot or base triple. In previous work, we investigated asymptotic combinatorics of both random saturated structures and of quasi-random saturated structures, where the latter are constructed by a natural stochastic process. RESULTS: We prove that for quasi-random saturated structures with the uniform distribution, the asymptotic expected number of external loops is O(logn) and the asymptotic expected maximum stem length is O(logn), while under the Zipf distribution, the asymptotic expected number of external loops is O(log2n) and the asymptotic expected maximum stem length is O(logn/log logn). CONCLUSIONS: Quasi-random saturated structures are generated by a stochastic greedy method, which is simple to implement. Structural features of random saturated structures appear to resemble those of quasi-random saturated structures, and the latter appear to constitute a class for which both the generation of sampled structures as well as a combinatorial investigation of structural features may be simpler to undertake.

On the page number of RNA secondary structures with pseudoknots.

Let S denote the set of (possibly noncanonical) base pairs {i, j } of an RNA tertiary structure; i.e. {i, j} ∈ S if there is a hydrogen bond between the ith and jth nucleotide. The page number of S, denoted π(S), is the minimum number k such that Scan be decomposed into a disjoint union of k secondary structures. Here, we show that computing the page number is NP-complete; we describe an exact computation of page number, using constraint programming, and determine the page number of a collection of RNA tertiary structures, for which the topological genus is known. We describe an approximation algorithm from which it follows that ω(S) ≤ π(S) ≤ ω(S) ・log n,where the clique number of S, ω(S), denotes the maximum number of base pairs that pairwise cross each other.

Asymptotics of canonical and saturated RNA secondary structures.

It is a classical result of Stein and Waterman that the asymptotic number of RNA secondary structures is 1.104366 . n(-3/2) . 2.618034(n). In this paper, we study combinatorial asymptotics for two special subclasses of RNA secondary structures - canonical and saturated structures. Canonical secondary structures are defined to have no lonely (isolated) base pairs. This class of secondary structures was introduced by Bompfünewerer et al., who noted that the run time of Vienna RNA Package is substantially reduced when restricting computations to canonical structures. Here we provide an explanation for the speed-up, by proving that the asymptotic number of canonical RNA secondary structures is 2.1614 . n(-3/2) . 1.96798(n) and that the expected number of base pairs in a canonical secondary structure is 0.31724 . n. The asymptotic number of canonical secondary structures was obtained much earlier by Hofacker, Schuster and Stadler using a different method. Saturated secondary structures have the property that no base pairs can be added without violating the definition of secondary structure (i.e. introducing a pseudoknot or base triple). Here we show that the asymptotic number of saturated structures is 1.07427 . n(-3/2) . 2.35467(n), the asymptotic expected number of base pairs is 0.337361 . n, and the asymptotic number of saturated stem-loop structures is 0.323954 . 1.69562(n), in contrast to the number 2(n - 2) of (arbitrary) stem-loop structures as classically computed by Stein and Waterman. Finally, we apply the work of Drmota to show that the density of states for [all resp. canonical resp. saturated] secondary structures is asymptotically Gaussian. We introduce a stochastic greedy method to sample random saturated structures, called quasi-random saturated structures, and show that the expected number of base pairs is 0.340633 . n.

On realizing shapes in the theory of RNA neutral networks.

It is known (Reidys et al., 1997b. Bull. Math. Biol. 59(2), 339-397) that for any two secondary structures S,S' there exists an RNA sequence compatible with both, and that this result does not extend to more than two secondary structures. Indeed, a simple formula for the number of RNA sequences compatible with secondary structures S,S' plays a role in the algorithms of Flamm et al. (2001. RNA 7, 254-265) and of Abfalter et al. (2003. Proceedings of the German Conference on Bioinformatics, ) to design an RNA switch. Here we show that a natural extension of this problem is NP-complete. Unless P=NP, there is no polynomial time algorithm, which when given secondary structures S1,...,S(k), for k4, determines the least number of positions, such that after removal of all base pairs incident to these positions there exists an RNA nucleotide sequence compatible with the given secondary structures. We also consider a restricted version of this problem with a "fixed maximum" number of possible stars and show that it has a simple polynomial time solution.

Structural RNA has lower folding energy than random RNA of the same dinucleotide frequency.

We present results of computer experiments that indicate that several RNAs for which the native state (minimum free energy secondary structure) is functionally important (type III hammerhead ribozymes, signal recognition particle RNAs, U2 small nucleolar spliceosomal RNAs, certain riboswitches, etc.) all have lower folding energy than random RNAs of the same length and dinucleotide frequency. Additionally, we find that whole mRNA as well as 5'-UTR, 3'-UTR, and cds regions of mRNA have folding energies comparable to that of random RNA, although there may be a statistically insignificant trace signal in 3'-UTR and cds regions. Various authors have used nucleotide (approximate) pattern matching and the computation of minimum free energy as filters to detect potential RNAs in ESTs and genomes. We introduce a new concept of the asymptotic Z-score and describe a fast, whole-genome scanning algorithm to compute asymptotic minimum free energy Z-scores of moving-window contents. Asymptotic Z-score computations offer another filter, to be used along with nucleotide pattern matching and minimum free energy computations, to detect potential functional RNAs in ESTs and genomic regions.